NOTES AND MEMORANDA. 327 



such perfection, as to make it fully equal to the requirements of pi'ac- 

 tical mineralogy. Whilst si^eakiug on this point, it may be well to 

 give an illustration of the accuracy with which it is possible to 

 measure the index with the ajjparatus which I have now at disposal. 

 Thus, in the case of a sj)ecimen of quartz, about "372 inch thick, five 

 diti'ereut determinations of the index of the ordinary ray for the light 

 transmitted by red glass, which corresponds to the solar line c, were 

 1-5513, 1-5531, 1-5524, 1-5531 and 1-5513, so that no observation 

 differed more than a unit in the third place of decimals from the 

 mean value, which may therefore be looked upon as true to the third 



T 



place of decimals, assuming that the equation /a = needs no 



correction. 



There was no difficulty in thus proving that there is a slight but 

 well-marked difference in the index for different specimens. The 

 mean for five was 1 - 5543, whereas, according to Rudberg, it is 1 - 5418. 

 In a similar manner I found that my method invariably gave too high 

 a result in the case of other minerals. After many careful measure- 

 ments I came to the conclusion that this can be satisfactorily attri- 

 buted to the spherical aberration due to the introduction of a trans- 

 parent plate in front of the object-glass, as suggested by Professor 

 Stokes. The amount of this error depends partly on the index of 

 refraction, and partly on the special correction of each particular 

 object-glass ; and when great accuracy is desired, it is necessary to 

 construct a small table showing the amount that must be deducted in 

 each case. I thus find that, when using my f object-glass, if the 

 index is about 1-5 1 must deduct -0100, and when 2-0, must deduct 

 •0180. 



Having thus shown how accurately the index may be measured, it 

 may be well to briefly allude to some improvements in the apparatus. 

 I find two cross lines in the fucus of the eye lens very useful in 

 keejiing constant the focal adjustment of the eye itself. In adjusting 

 the focus of any object it is always arranged so that the cross lines are 

 also in sharp focus. Without this precaution there may be an im- 

 portant difference, according as the focus is adjusted by moving the 

 object-glass up or down. I have also found it desirable to take the 

 means of two or more sets of measurements made in slightly different 

 parts of the scale, so as to eliminate any error due to imperfect gradua- 

 tion. This is easily managed by moving the fine adjustment. It is 

 by adopting these precautions that I have been able to make such 

 concordant and accurate measurements as those given above in the case 

 of quartz, and to prove that the limit of error may be made very small. 



When first I commenced to apply my method to the study of 

 various minerals, with the view of comparing mathematical theory 

 with observation, I soon found that there were a few discrepancies. 

 For some time I thought it just possible that these might be due to 

 errors in the measurements, but I found that these discrepancies 

 became the more and more marked as by degrees I was able to remove 

 every api)arent source of error. The principal discrepancy is in the 

 case of bi-axial crystals like aragonite, but some are also met with in 



